Shear-Thickening Fluid: Why You Can Run on Cornstarch

The flow curve: what “thickening” actually means

Every fluid obeys a constitutive law linking the shear stress τ (force per area you apply) to the shear rate γ̇ (how fast one layer slides past the next). For an ordinary Newtonian fluid the two are simply proportional, τ = ηγ̇, and the viscosity η is a fixed material constant — water is water whether you stir it slowly or fast. Non-Newtonian fluids break that proportionality. A useful shorthand is the power law τ = Kγ̇ⁿ: when the index n < 1 the fluid is shear-thinning (it gets runnier as you push harder, like ketchup or blood), when n = 1 it is Newtonian, and when n > 1 it is shear-thickening.

Shear thickening itself comes in two flavors. In continuous shear thickening (CST), the effective viscosity climbs smoothly with shear rate. In discontinuous shear thickening (DST) — the dramatic case behind oobleck — the viscosity leaps by one to two orders of magnitude across a narrow band of stress, so steeply that the flow curve of stress versus shear rate becomes S-shaped, with a stretch of negative slope that no stable steady flow can sit on. This is measured on a rotational rheometer (a cone-and-plate or Couette cell that shears a thin film and reads back the torque), which is how the jump is turned from a party trick into a quantitative flow curve.

A crowded suspension living next to jamming

Oobleck is a dense suspension: roughly half its volume is solid. Cornstarch granules 5–20 µm across are packed to a solids volume fraction φ of about 0.49–0.58 — uncomfortably close to random close packing, φ_RCP ≈ 0.64, the density at which frictionless spheres run out of room and lock up. The entire effect lives in that narrow gap between “mostly full” and “completely jammed.”

Two competing sets of forces decide whether the grains can slide past each other. Keeping them apart is a short-range repulsion — electrostatic double-layer charge, adsorbed polymer, and, crucially, lubrication films of water that must be squeezed out of the gap before two grains touch (a viscous resistance closely related to Stokes drag). Pushing them together is the external shear stress. For colloids one gauges the balance with the Péclet number, Pe = 6πη_fa³γ̇ / k_BT, comparing shear to thermal Brownian jostling. But cornstarch grains are microns wide and effectively non-Brownian — Pe is enormous even at a gentle stir — so the natural control parameter is not shear rate but stress. There is a characteristic onset stress σ* ≈ F*/a², set by the repulsive force F* holding a lubrication gap open. For cornstarch σ* falls in the range ~1–100 Pa, and because F* typically scales with particle size while the stress carries a 1/a², larger grains thicken at lower stress.

The mechanism: lubricated grains flip to frictional contact

Below the onset stress, the grains never actually touch. Thin lubrication films hold them apart, they roll and glide around one another, and the suspension flows as a viscous liquid. The moment the applied stress exceeds σ*, the compressive force squeezes those water films thinner than the surface roughness, the repulsive barrier is overwhelmed, and neighboring grains slam into direct solid-on-solid contact. Contact means friction. Frictional grains cannot simply slide past each other; instead they build a network of force chains — anisotropic chains of grains pressing together along the compression axis (roughly 45° to the flow) that carry load like the trusses of a momentary bridge. When that contact network percolates across the sample, the suspension jams into a transient solid.

The modern quantitative picture is the Wyart–Cates model (2014), built on particle simulations by Seto, Mari, Denn and Morris. The jamming fraction is not a single number but slides with stress: φ_J(σ) = φ₀(1−f) + φ_mf, where f(σ) ≈ exp(−σ*/σ) is the fraction of contacts that have gone frictional. At low stress f ≈ 0 and jamming waits until the frictionless point φ₀ ≈ 0.64; at high stress f → 1 and jamming arrives early, at the lower frictional point φ_m ≈ 0.55–0.58. The viscosity diverges as η ∝ (φ_J − φ)⁻². If your suspension sits in the window φ_m < φ < φ₀, then as you raise the stress φ_J slides down through φ — the viscosity blows up and you get DST or outright shear jamming. This friction paradigm superseded the older hydrocluster model of Brady, Bossis and Wagner (1980s–2000s), in which purely hydrodynamic lubrication forces glued transient particle clusters together; hydroclusters explain mild CST in colloids, but the abrupt DST of dense suspensions is a friction story.

Reynolds dilatancy and why the boundary matters

There is an older, complementary idea that explains the solid feel of oobleck and of wet sand. In 1885 Osborne Reynolds pointed out that a densely packed bed of grains cannot be sheared without dilating — expanding its volume — because grains have to ride up and over one another to move at all. Step on wet sand at the beach and a pale, dry-looking halo appears around your foot: the pack dilated, sucking water down into the newly opened pores. That expansion is normally free. But in a suspension the grains are confined — by the container walls, and at a free surface by surface tension pulling the air–water interface taut. When shear demands dilation that the boundary refuses to allow, the frustration shows up as a large confining pressure that clamps the grains together and makes the whole packing rigid.

Eric Brown and Heinrich Jaeger (Reports on Progress in Physics, 2014) argued that this frustrated dilation against a hard boundary is essential to the most spectacular demonstrations: the transient solid is only as strong as the boundary it can push against. It is why a thin puddle you can crack with a hammer becomes a spreading splash if there is nothing beneath it, and why the effect is reversible — remove the confinement or the stress and the grains relax back to a flowing pack. Friction sets when the grains lock; boundaries set how much stress that locked network can bear.

Running on oobleck: impact-activated jamming fronts

Running works and standing fails for a reason with a stopwatch attached. When your foot strikes the surface, it does not just jam the fluid directly beneath it. Experiments by Scott Waitukaitis and Heinrich Jaeger (Nature, 2012) drove a rod into cornstarch and used high-speed imaging to reveal a dynamic jamming front: a wave of solidification that races ahead of the intruder, several times faster than the intruder itself, sweeping loose grains into a growing rigid plug and adding their mass to it. The plug behaves like a mushrooming solid column glued to your foot.

If that front reaches the rigid bottom of the pool before your foot has traveled far, the stress is transmitted straight through the solidified column to the ground, which shoves back and supports your weight — you skitter across. But the solid state only survives while the stress lasts. Stand still and the front never forms; over a second or two the force chains relax, the plug re-liquefies, and you sink like any dense mud. The whole trick is a race between the propagation of the jamming front and the relaxation of the frictional network. Fast, hard, brief impact wins; slow, steady load loses.

Measuring it — and the ways it misbehaves

Because DST is fundamentally a stress-controlled transition, the cleanest data come from stress-controlled rheometry that traces the full flow curve, including the treacherous negative-slope branch of the S-curve. That branch is mechanically unstable, and dense suspensions exploit every available instability to avoid it. Real samples show shear banding (the flow splits into coexisting fast and slow layers), vorticity banding, oscillatory or stick-slip stress fluctuations, and, at the most violent thickening, the suspension can fracture or dewet and climb out of the gap entirely. Edge fracture and the pull of the free surface make DST notoriously hard to measure reproducibly, which is part of why its mechanism was debated for decades.

A few clean signatures distinguish genuine shear thickening from look-alikes. It is reversible and rate-independent in stress: lower the stress and full fluidity returns, unlike thixotropic pastes whose thickness depends on their recent history. It is not shear-thinning ketchup, which merely takes an initial yield stress to start flowing and then runs freely. And it is not a chemical gel or a glass, whose rigidity persists without any applied load. Oobleck is only solid while you are hitting it.

Liquid body armor and adaptive materials

A material that is soft and flexible until it is struck hard is exactly what protective gear wants. Norman Wagner's group at the University of Delaware, working with the U.S. Army Research Laboratory, developed shear-thickening fluid (STF) armor by impregnating woven Kevlar with a suspension of fumed silica nanoparticles in polyethylene glycol. In normal wear the fabric drapes and bends; on ballistic or knife impact the STF thickens within microseconds, coupling the fibers together and spreading the load over a wider area, so a few STF-soaked layers can match the stab and puncture resistance of many more layers of dry Kevlar while staying far more flexible.

The same rate-dependent stiffening shows up across engineering. Impact-protective foams and pads (the best-known commercial example is D3O) stay pliable until a blow. Fluid-filled speed bumps have been trialed that stay soft under a slow car and jam rigid under a fast one, and researchers have proposed shear-thickening pothole and bridge fillers along the same lines. Open questions remain — how to predict σ* and the strength of the jammed state from particle shape, roughness and surface chemistry; how force chains rearrange under real, chaotic impacts; and how to tune φ and friction to place the onset exactly where an application needs it. The kitchen demonstration is settled physics; engineering it on demand is still an active frontier.

Four flow behaviors, distinguished by how viscosity responds to shear rate. Only dense suspensions near jamming show the abrupt discontinuous jump.

Fluid class	Viscosity η vs. shear rate γ̇	Everyday example	Microscopic mechanism
Shear-thinning (pseudoplastic)	Falls (power-law index n < 1)	Ketchup, blood, paint, polymer melts	Aligned/entangled structure breaks down under flow
Newtonian	Constant (n = 1)	Water, air, glycerol, honey	τ = ηγ̇; no internal microstructure change
Continuous shear-thickening (CST)	Rises smoothly (n > 1)	Dilute cornstarch, colloidal silica	Hydrodynamic “hydroclusters” increase dissipation
Discontinuous shear-thickening (DST)	Jumps by 10–100× at a critical stress	Dense oobleck, STF body-armor fluid	Stress-activated frictional contacts → shear jamming